Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Maths, Physics and chemistry books are stored on a library
[#permalink]
Show Tags
Updated on: 02 Apr 2014, 21:09
2
16
00:00
A
B
C
D
E
Difficulty:
45% (medium)
Question Stats:
73% (03:27) correct 27% (03:19) wrong based on 371 sessions
HideShow timer Statistics
Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability, that a book selected at random is either a hard cover book or a chemistry book?
Maths, Physics and chemistry books are stored on a library shelf that can accomodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the prob, that a book selected at random is either a hard cover book or a chemistry book?
Chemistry books: 2 Physics books: 6 Math books: 12
P(AuB) - P(AnB) = 21/50 (since either means that we don't want both)
What is wrong here? (OA: 9/20)
Everything is correct except this: P(AnB) = P(A)*(B) = (1/10)*(2/5) = 2/50 P(AnB) is given by the product of individual probabilities when the events are independent. How many Chemistry books are hardcover? There are total 8 hardcovers and 7 belong to Math and Physics. This means there is only 1 Chemistry hardcover book out of total 20 books. So P(AnB) = 1/20
Re: Maths, Physics and chemistry books are stored on a library
[#permalink]
Show Tags
30 Mar 2014, 09:32
5
2
First phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations:
m + p + c = 20 (since 4/5 of the 25 spots are full of books)
m = 2p
p = 4 + c
From that, you can use Substitution to get everything down to one variable.
c = p - 4
m = 2p
p = p
Then (p - 4) + 2p + p = 20, so 4p = 24 and p = 6. That means that there are 12 math, 6 physics, and 2 chemistry books on the shelf.
With those numbers, you also know that there are 8 total hardcovers, 1 of which is chemistry. So if your goal is to get either a hardcover or a chemistry, there are 9 ways to "win" - either one of the 7 hardcovers that aren't chemistry or the two chemistry books. So out of the 20 total, 9 provide the desired outcome, making the answer E.
Note - a common trap answer here is A, as people forget that "2 chem + 8 hard" double counts the one book that is "both". Venn Diagram logic can be helpful to avoid that trap, or in cases like this with relatively small numbers it may be even more convenient to just write out the possibilities.
Maths, Physics and chemistry books are stored on a library shelf that can accomodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 4 hard-cover books among the maths and physics books. What is the prob, that a book selected at random is either a hard cover book or a chemistry book?
1/10 3/20 1/5 1/4 9/20
the shelf has the capacity of 25 books, 20% empty (5 books), the shelf has 20 books
So the shelf only has 12 math, 6 phys, 2 chem books
If there are 12 soft covers and 8 hard covers, and 4 hard covers are math/phys, then 4 hard cover must be chemistry, BUT there are only 2 chemistry books.
Maths, Physics and chemistry books are stored on a library shelf that can accomodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the prob, that a book selected at random is either a hard cover book or a chemistry book?
Chemistry books: 2 Physics books: 6 Math books: 12
Concentration: Entrepreneurship, International Business
GMAT 1: 650 Q49 V30
GPA: 3.5
WE: Engineering (Computer Software)
Re: Maths, Physics and chemistry books are stored on a library
[#permalink]
Show Tags
01 Apr 2014, 22:12
@GDR29,
Thanks for the explanation but I have one doubt.
We know that there are two chemistry books and there is no information like atleast each of Maths, Physics and Checmistry has to be either soft or hard covered. In such case, there will be two chemistry books which may be hard covered.
Re: Maths, Physics and chemistry books are stored on a library
[#permalink]
Show Tags
02 Apr 2014, 06:22
2
Hi guys, After knowing there are 20 books on the shelve, I've just used the "Among all the books, 12 books are soft cover and the remaining are hard-cover" info. Using this info you get that 8/20 books are hard cover... and at least one book has to be chemestry, so the chances of getting either a hard cover book or a chemestry one have to be higher than 8/20 --- only alternative is E) 9/20 What do you think? Thanks!
Re: Maths, Physics and chemistry books are stored on a library
[#permalink]
Show Tags
02 Apr 2014, 21:09
nishant.1987 wrote:
@GDR29,
Thanks for the explanation but I have one doubt.
We know that there are two chemistry books and there is no information like atleast each of Maths, Physics and Checmistry has to be either soft or hard covered. In such case, there will be two chemistry books which may be hard covered.
Please advise.
There is a typo in the question given. You are given that there are 12 softcover books (which means there are 8 hard cover books). You also given that 7 of the hardcover books are either Math or Physics. So there is only 1 Chemistry hard cover book.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT self-study has never been more personalized or more fun. Try ORION Free!
Re: Maths, Physics and chemistry books are stored on a library
[#permalink]
Show Tags
02 Apr 2014, 21:12
easycheesy wrote:
Hi guys, After knowing there are 20 books on the shelve, I've just used the "Among all the books, 12 books are soft cover and the remaining are hard-cover" info. Using this info you get that 8/20 books are hard cover... and at least one book has to be chemestry, so the chances of getting either a hard cover book or a chemestry one have to be higher than 8/20 --- only alternative is E) 9/20 What do you think? Thanks!
That's correct. Note that we do analyze the rest of the data to say that the required probability has to be greater than 8/20 since it is possible that all Chem books are hardcover and hence already a part of the 8 books. But, to say that the required probability is "greater than or equal to" 8/20, all we need is "Among all the books, 12 books are soft cover and the remaining are hard-cover".
There is only one option greater than or equal to 8/20.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT self-study has never been more personalized or more fun. Try ORION Free!
Re: Maths, Physics and chemistry books are stored on a library
[#permalink]
Show Tags
11 May 2014, 23:29
alimad wrote:
Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability, that a book selected at random is either a hard cover book or a chemistry book?
8 + 2c + 4 + c + c = 20 4c + 12 = 20 4c = 8 c = 2 , P = 6, M = 12
Please assist further. Thanks
Hello I am not good at probability, but somehow got this answer right . Could you please explain if the approach used by me is correct or it was just a stroke of luck that i got it right..
Number of Math+Physics+Chemistry books= 25 - ((20/100)*25) = 20 Hence, since M=2P, P=4+C, (4+C)+C+2(4+C)=20 Therefore, M=12, C=2, P=6
Probability of getting a chemistry book = 2/20 = 1/10 Probability of getting a Hardcover book = P(getting a math or phy book) * P( getting a hardcover book from math or phy books) = (18/20 )*(7/18) = 7/20
Therefore, P(Getting chemistry or hardcover book) = (1/10)+(7/20) = 9/20
I am really doubtful about the red colored approach. Please guide.
Re: Maths, Physics and chemistry books are stored on a library
[#permalink]
Show Tags
12 May 2014, 02:32
1
khushboobhatia wrote:
alimad wrote:
Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability, that a book selected at random is either a hard cover book or a chemistry book?
8 + 2c + 4 + c + c = 20 4c + 12 = 20 4c = 8 c = 2 , P = 6, M = 12
Please assist further. Thanks
Hello I am not good at probability, but somehow got this answer right . Could you please explain if the approach used by me is correct or it was just a stroke of luck that i got it right..
Number of Math+Physics+Chemistry books= 25 - ((20/100)*25) = 20 Hence, since M=2P, P=4+C, (4+C)+C+2(4+C)=20 Therefore, M=12, C=2, P=6
Probability of getting a chemistry book = 2/20 = 1/10 Probability of getting a Hardcover book = P(getting a math or phy book) * P( getting a hardcover book from math or phy books) = (18/20 )*(7/18) = 7/20
Therefore, P(Getting chemistry or hardcover book) = (1/10)+(7/20) = 9/20
I am really doubtful about the red colored approach. Please guide.
Your approach is correct. Though the red part should be {the probability of getting a hardcover math or physics book}.
_________________
Re: Maths, Physics and chemistry books are stored on a library
[#permalink]
Show Tags
10 Oct 2014, 18:55
VeritasPrepKarishma wrote:
Mackieman wrote:
Please help me with this one.
Maths, Physics and chemistry books are stored on a library shelf that can accomodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the prob, that a book selected at random is either a hard cover book or a chemistry book?
Chemistry books: 2 Physics books: 6 Math books: 12
P(AuB) - P(AnB) = 21/50 (since either means that we don't want both)
What is wrong here? (OA: 9/20)
Everything is correct except this: P(AnB) = P(A)*(B) = (1/10)*(2/5) = 2/50 P(AnB) is given by the product of individual probabilities when the events are independent. How many Chemistry books are hardcover? There are total 8 hardcovers and 7 belong to Math and Physics. This means there is only 1 Chemistry hardcover book out of total 20 books. So P(AnB) = 1/20
Now P(AuB) = 1/10 + 2/5 - 1/20 = 9/20
Hi Karishma. request you to please help me by explaining why the solution is also accounting for the book which is both chemistry and hard cover when the question stem clearly asks we need to select only books which are "Either" chem or hard cover.
_________________
Sometimes standing still can be, the best move you ever make......
Re: Maths, Physics and chemistry books are stored on a library
[#permalink]
Show Tags
12 Oct 2014, 19:57
aadikamagic wrote:
Hi Karishma. request you to please help me by explaining why the solution is also accounting for the book which is both chemistry and hard cover when the question stem clearly asks we need to select only books which are "Either" chem or hard cover.
In Math, 'either or' is interpreted a little differently - it includes the elements which lie in both sets too. "Either Chem or hardcover" means "Chemistry books or hardcover books or both".
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT self-study has never been more personalized or more fun. Try ORION Free!
Re: Maths, Physics and chemistry books are stored on a library
[#permalink]
Show Tags
15 Aug 2015, 03:10
This is a brilliant way of thinking. I really need to develop such ability to get +750. Thanks for sharing easycheesy Kudos sent
easycheesy wrote:
Hi guys, After knowing there are 20 books on the shelve, I've just used the "Among all the books, 12 books are soft cover and the remaining are hard-cover" info. Using this info you get that 8/20 books are hard cover... and at least one book has to be chemestry, so the chances of getting either a hard cover book or a chemestry one have to be higher than 8/20 --- only alternative is E) 9/20 What do you think? Thanks!
Re: Maths, Physics and chemistry books are stored on a library
[#permalink]
Show Tags
19 Jul 2018, 22:50
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
close
73% (03:27) correct 
